From the last thread:
From Costanza's original thread (entire text):
"This is for anyone in the LessWrong community who has made at least some effort to read the sequences and follow along, but is still confused on some point, and is perhaps feeling a bit embarrassed. Here, newbies and not-so-newbies are free to ask very basic but still relevant questions with the understanding that the answers are probably somewhere in the sequences. Similarly, LessWrong tends to presume a rather high threshold for understanding science and technology. Relevant questions in those areas are welcome as well. Anyone who chooses to respond should respectfully guide the questioner to a helpful resource, and questioners should be appropriately grateful. Good faith should be presumed on both sides, unless and until it is shown to be absent. If a questioner is not sure whether a question is relevant, ask it, and also ask if it's relevant."
Meta:
- How often should these be made? I think one every three months is the correct frequency.
- Costanza made the original thread, but I am OpenThreadGuy. I am therefore not only entitled but required to post this in his stead. But I got his permission anyway.
Meta:
- I still haven't figured out a satisfactory answer to the previous meta question, how often these should be made. It was requested that I make a new one, so I did.
- I promise I won't quote the entire previous threads from now on. Blockquoting in articles only goes one level deep, anyway.
't Hooft's latest paper is the first in which he maps a full QFT to a CA, and the QFT in question is a free field theory. So I think that in this case he evades Bell's theorem, quantum complexity theorems, etc, by working in a theory where physical detectors, quantum computers, etc don't exist, because interactions don't exist. It's like how you can evade the incompleteness theorems if your arithmetic only has addition but not multiplication. Elsewhere he does appeal to superselection / cosmological initial conditions as a way to avoid cat states (macroscopic superpositions), but I don't see that playing a role here.
The mapping itself has something to do with focusing on the fractional part of particle momentum as finite, and avoiding divergences by focusing on a particular subspace. It's not a trivial result. But extending it to interacting field theory will require new ideas, e.g. making the state space of each individual cell in the CA into a Fock space, or permitting CTCs in the CA grid. Surely you need radical ingredients like that in order to recover the full quantum state space...